3 papers
math.DS2026
Design of Hierarchical Excitable Networks
Sören von der Gracht, Alexander Lohse
We provide a method to systematically construct vector fields for which the dynamics display transitions corresponding to a desired hierarchical connection structure. This structur…
math.DS2026
Complete heteroclinic networks derived from graphs consisting of two cycles
Sofia B. S. D. Castro, Alexander Lohse
We address the question how a given connection structure (directed graph) can be realised as a heteroclinic network that is complete in the sense that it contains all unstable mani…
math.DS2025
How many points converge to a heteroclinic network in an aperiodic way?
Christian Bick, Alexander Lohse
Homoclinic and heteroclinic connections can form cycles and networks in phase space, which organize global phenomena in dynamical systems. On the one hand, stability notions for (o…